{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import time, sys\n",
    "\n",
    "# Import the Qiskit \n",
    "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister, QiskitError\n",
    "from qiskit import execute, IBMQ, BasicAer, transpiler, Aer\n",
    "from qiskit.providers.ibmq import least_busy\n",
    "from qiskit.tools.monitor import job_monitor\n",
    "from qiskit.mapper import Layout"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define your backend"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "qasm_simulator\n"
     ]
    }
   ],
   "source": [
    "# execute on the qasm simulator\n",
    "import qiskit\n",
    "backend = qiskit.Aer.get_backend('qasm_simulator')\n",
    "print(backend)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define the UCCSD ansatz circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "def get_ucc_ansatz(theta):\n",
    "    circuit = QuantumCircuit(2, 2)\n",
    "    circuit.x(0)\n",
    "    circuit.ry(theta, 1)\n",
    "    circuit.cx(1, 0)\n",
    "    return circuit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define the naive measurement circuits\n",
    "more automations can be done in here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define the number of shots\n",
    "shots = 5000\n",
    "\n",
    "def measure_zi(theta):\n",
    "    circuit = get_ucc_ansatz(theta)\n",
    "    circuit.measure(0, 0)\n",
    "    circuit.measure(1, 1)\n",
    "    job = qiskit.execute(circuit, backend=backend, shots=shots)\n",
    "    #job_monitor(job)\n",
    "    counts = job.result().get_counts(circuit)\n",
    "    return (counts.get('00', 0) + counts.get('10', 0) - counts.get('11', 0) - counts.get('01', 0))/shots\n",
    "\n",
    "\n",
    "def measure_iz(theta):\n",
    "    circuit = get_ucc_ansatz(theta)\n",
    "    circuit.measure(0, 0)\n",
    "    circuit.measure(1, 1)\n",
    "    job = qiskit.execute(circuit, backend=backend, shots=shots)\n",
    "    #job_monitor(job)\n",
    "    counts = job.result().get_counts(circuit)\n",
    "    return (counts.get('00', 0) + counts.get('01', 0) - counts.get('10', 0) - counts.get('11', 0))/shots\n",
    "\n",
    "\n",
    "def measure_xx(theta):\n",
    "    circuit = get_ucc_ansatz(theta)\n",
    "    circuit.h(0)\n",
    "    circuit.h(1)\n",
    "    circuit.measure(0, 0)\n",
    "    circuit.measure(1, 1)\n",
    "    job = qiskit.execute(circuit, backend=backend, shots=shots)\n",
    "    #job_monitor(job)\n",
    "    counts = job.result().get_counts(circuit)\n",
    "    return (counts.get('00', 0) + counts.get('11', 0) - counts.get('01', 0) - counts.get('10', 0))/shots\n",
    "\n",
    "\n",
    "def measure_yy(theta):\n",
    "    circuit = get_ucc_ansatz(theta)\n",
    "    circuit.h(0)\n",
    "    circuit.sdg(0)\n",
    "    circuit.h(1)\n",
    "    circuit.sdg(1)\n",
    "    circuit.measure(0, 0)\n",
    "    circuit.measure(1, 1)\n",
    "    job = qiskit.execute(circuit, backend=backend, shots=shots)\n",
    "    #job_monitor(job)\n",
    "    counts = job.result().get_counts(circuit)\n",
    "    return (counts.get('00', 0) + counts.get('11', 0) - counts.get('01', 0) - counts.get('10', 0))/shots\n",
    "\n",
    "def measure_hamiltonian(theta):\n",
    "    return 5.9 + .22 * measure_zi(theta) - 6.1 * measure_iz(theta) - 2.14 * measure_xx(theta) - 2.14 * measure_yy(theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### run the experiment with different theta value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[12.25424, 13.421864000000001, 12.653080000000001, 10.20152, 6.443704000000001, 2.6195520000000014, -0.35922399999999904, -1.736223999999999, -1.073368, 1.660952, 5.332592000000002, 9.200616000000002]\n",
      "[-3.141592653589793, -2.6179938779914944, -2.0943951023931957, -1.570796326794897, -1.0471975511965983, -0.5235987755982996, -8.881784197001252e-16, 0.5235987755982978, 1.0471975511965965, 1.5707963267948948, 2.094395102393194, 2.617993877991493]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "values = []\n",
    "thetas = []\n",
    "for theta in np.arange(-np.pi, np.pi, np.pi/6):\n",
    "    values.append(measure_hamiltonian(theta))\n",
    "    thetas.append(theta)\n",
    "print(values)\n",
    "print(thetas)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### plot the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.plot(thetas, values, 'g^')\n",
    "plt.plot(thetas, values)\n",
    "plt.xlabel('theta values')\n",
    "plt.ylabel('energy sums')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define the simultaneous measurement circuits\n",
    "more automations can be done in here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define the number of shots\n",
    "shots = 5000\n",
    "\n",
    "def measure_zi_and_iz(theta):\n",
    "    circuit = get_ucc_ansatz(theta)\n",
    "    circuit.measure(0, 0)\n",
    "    circuit.measure(1, 1)\n",
    "    job = qiskit.execute(circuit, backend=backend, shots=shots)\n",
    "    #job_monitor(job)\n",
    "    counts = job.result().get_counts(circuit)\n",
    "    zi = (counts.get('00', 0) + counts.get('10', 0) - counts.get('11', 0) - counts.get('01', 0))/shots\n",
    "    iz = (counts.get('00', 0) + counts.get('01', 0) - counts.get('10', 0) - counts.get('11', 0))/shots\n",
    "    return zi, iz\n",
    "\n",
    "def measure_xx_and_yy(theta):\n",
    "    circuit = get_ucc_ansatz(theta)\n",
    "    circuit.h(1)\n",
    "    circuit.cx(1, 0)\n",
    "    circuit.cz(0, 1)\n",
    "    circuit.h(0)\n",
    "    circuit.h(1)\n",
    "    circuit.measure(0, 0)\n",
    "    circuit.measure(1, 1)\n",
    "    job = qiskit.execute(circuit, backend=backend, shots=shots)\n",
    "    #job_monitor(job)\n",
    "    counts = job.result().get_counts(circuit)\n",
    "    xx = (counts.get('00', 0) + counts.get('10', 0) - counts.get('11', 0) - counts.get('01', 0))/shots\n",
    "    yy = (counts.get('00', 0) + counts.get('01', 0) - counts.get('10', 0) - counts.get('11', 0))/shots\n",
    "    return xx, yy\n",
    "\n",
    "def measure_simultaneously_hamiltonian(theta):\n",
    "    xx, yy = measure_xx_and_yy(theta)\n",
    "    zi, iz = measure_zi_and_iz(theta)\n",
    "    return 5.9 + .22 * zi - 6.1 * iz - 2.14 * xx - 2.14 * yy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### run the experiment with different theta value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[12.194319999999998, 13.55516, 12.660888000000002, 10.039712000000002, 6.459328, 2.4680560000000007, -0.44824799999999904, -1.6949919999999998, -1.0587199999999994, 1.5412800000000004, 5.355040000000001, 9.303232]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "values2 = []\n",
    "for theta in np.arange(-np.pi, np.pi, np.pi/6):\n",
    "    values2.append(measure_hamiltonian(theta))\n",
    "print(values2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### plot the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.plot(thetas, values2, 'g^')\n",
    "plt.plot(thetas, values2)\n",
    "plt.xlabel('theta values')\n",
    "plt.ylabel('energy sums')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculate the difference between the naive and simultaneous methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "value_diff = []\n",
    "for theta in range(len(thetas)):\n",
    "    value_diff.append(values[theta] - values2[theta])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.plot(thetas, value_diff, 'g^')\n",
    "plt.plot(thetas, value_diff)\n",
    "plt.xlabel('theta values')\n",
    "plt.ylabel('energy sums')\n",
    "plt.title('difference between simultaneous and naive for simulator')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Superimpose the two"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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71Mf3Kr+wfXyEOk3a0vTR8QQP3cOpHl9iL1ONB9On8fTGvqRN6sdLb4/g6amrmLM+ilOJaR5+UUrlT0eOHKFIkSLcc889vPTSS6xbt+6KlxEWFkZkZCQOh4NDhw6xevXq/0wTHBxMfHz8ufunT5+mbNmy2O12lixZwoEDl+5VulixYlSrVo2ZM2cCzhbGhg0bALjuuuuYPn064Cw0Z1s5YWFhREREADBv3jzS0527oQ8cOEBoaCiDBw/moYceuqrXfDnaQnDDmei9HJ8ykOqJkSzxaY3c/ClPN63n2ZXYAynZ+m5ofTec3Idj7fe0WT+VG5I/4uSub5i1rR39HR0pWaUhneuVpXO9slzfKIijR/+7ayk0FLdaK0rlhtDQ7A8gh4Ze/TI3bdrESy+9hI+PD3a7na+++ooXX3zxipbRtm1bqlWrRv369alXrx7NmjX7zzSlS5embdu2NGjQgJ49ezJkyBBuvvlmGjZsSIsWLahbt+5l1zN16lQee+wxRowYQXp6OnfccQeNGzdm9OjRDBw4kFGjRhESEsKECRMAGDx4MH369KFx48b06NGDokWLArB06VJGjRqF3W4nKCiI77///operzvE5KMzXVq0aGFyc4Ac43Cwbv5Y6qx7G2MMS6q9QOc7nqVowNV1HHXFHJmw+0/Mukmw4zfEZLDFVo+JKe1YkNma06dKkbw7lMRDhrS2j8OsGZDgPJcvH72tKh/atm0b9ep5+EeR8ojs3hsRiTDGtLjcvNpCuIhDUYc4MvVxWiUvZ4vvNfjeOpbe9RrmbggfG9TuhtTuBgnHYMM0rlk3mVEnxvFuwBRmJHdgVvPr+PO6X0mzrYD2w2HhmNzNqJQqMPQYwgXSMhzMmz0Z/2/a0SzpbyJqPU3dV5ZTJ7eLwYWCykLbZ+DJNTDod+wN+3FL0WX8XOQ1/vb5i1oINPsOgnRfkVLq6mhByGLNriMs+OBeem96kgz/Ypy593ea3z0cm28eakiJQJXW0HcM5T/aweD9rSiPMJdAitkysN001OqESql8SgsCEJeUxudTZlJycmduSZvPodr3U+GlVZSu2dLqaJcU75fI+EoruE2SqIkPU7FD3an4VtG+k5RSV65QFwRjDHPWHWDKqKd5bNcjhPqnk3LnLCrf9TnYA62Od1mBPYaDOFgumTxDCr2w8zY2Au58gaNndCQrpdSVKbQFYW9sAs+N/ZlKP9/Gk2YaSTV6EvzcagLqdLU6mtvqdAkHX+e1CV+RzjjSGIqdPgERDJywhoTUDIsTKqXykzy0c9zzypXL5vxnWyYVOu3hvlbjecc2CbufHcfN4yjeqL9z/3w+sv6R9ec/kJEGk25m0pFI+h7byONT/fn2/hZ6pbMq9L7++muKFCni8St7C5oC/U1xYTHwr3yCBg/O57tWj/GebSz2Ss3wezIcn8YD8l0xyJavHwyYjK1oaaYHf86WnbsZNmcz+elaE1VwWTm07KOPPqrFwA0FuiCcJWUO4Pt8c/rfM4o/yz5NRzZAtxH4DVoAJSpbHc+zgsrCHVMpmhHH3LJj+WntPr74nx5kVtYbvnw4fx38i+HLhud4WRfrbvqbb76hZcuWNG7cmFtvvZWkJOf4I2+++SYffvgh27dv59prrz1vOQ0bOk8pj4iIoEOHDjRv3pzu3bsTHR2d45z5TW6MmPadiBwTkc1ZHhslIttFZKOIzBGREt7MUKL/c3wevJXv/b4i5ngFWo5bCtc9BT4FtB5WaAp9xlDpTCQTy83io8U7mR0RZXUqVYhFx0czIXICDuNgQuQEj7QSsutuul+/fqxZs4YNGzZQr149vv32vPG4qFu3Lmlpaezbtw+AGTNmMGDAANLT03nqqaeYNWsWERERDBo0iFdffTXHGfOb3PhGnAj0uOCxxUADY0wjYCfwf15be1A0n5dexCPYGeXI5Npp09l0rIHXVpdnNLwN2j5L27h5vFYunCGzN/L37vw/MJ3Kn4YvH47DOHvwzDSZHmklZNfd9ObNm2nXrh0NGzZk6tSpbNmy5T/z9e/fnxkzZgD/FoQdO3awefNmunbtSpMmTRgxYgRRUYXvR1RuDKG5HDh5wWOLjDFnT4H5B6jktQAdhvOmyaAzSbxs0klt+4HXVpXndH4danZl0Jmv6FNyP49OjmB7zBmrU6lC5mzrIC3TeUZcWmaaR1oJF3Y3nZGRwQMPPMAXX3zBpk2beOONN7Lt0nrAgAH8+OOP7Ny5ExGhVq1aGGO45ppriIyMJDIykk2bNrFo0aIc5cuP8sI+k0HArxd7UkQeFpG1IrI2Njb2ihZcplo0NJnAHt9Ulkqm8xTNphMoE1ZIunfwscGt45GSYXzg+JDqficYOGEN0aeTrU6mCpGsrYOzPNVKuFB8fDzly5cnPT2dqVOnZjtNjRo1sNlsDB8+nAEDBgBQp04dYmNjCQ8PByA9PT3b1kVBZ2lBEJFXgQwg+3cOMMaMM8a0MMa0CAkJuaLl3z56OH4B538Q/QIy6f+F5z+IeVZgCbhzOjZHOtOLfUF6SiIDJ6whPiX98vMq5QHhUeHnWgdnpWWmsTJqpcfXNXz4cFq1akXbtm0v2TX1gAEDmDJlCv379wecI6zNmjWLIUOG0LhxY5o0acLKlZ7Pl9flSvfXIhIGzDfGNMjy2APAI0BnY0ySO8u50u6vm45tSmTMf0cqalKuyX/P4S/odi6CH/pzrMqNXLf7btrUKMN3D7TUaxTUVdHur/OufNf9tYj0AF4GOrhbDK5GofvSv5Ta3aDLG5T9401+alST3pGtGPrTJj64rZGO36yUAnLntNNpQDhQR0SiRORB4AsgGFgsIpEi8rW3cyig7bPQ4FYabf+cT5vGMDMiis/+3GV1KqVUHuH1FoIx5s5sHv42m8eUt4lA7y/gxG767HmDnQ3G8Okfu6hYIpDbWxSwC/SU1xljtHWZx+T0EIDuQC5s/IrAgKmIPYCXTr5F9xoB/N9Pm1ix68rO4FKFW0BAACdOnNBuUfIQYwwnTpwgICDgqpehYyoXVgfCYdLNZIS1p/eJpzgYl8aPj7ShfoViVidT+UB6ejpRUVHZnuevrBMQEEClSpWw288f993dg8paEAqztRNg/rMkNH+cLpu6ADDniesoXzzvjwWhlHKfuwVBdxkVZi0GQsuHCIr4ktnXR5GYmsHACWs4o9coKFUoaUEo7Hq8D1XbUnH5y0zuaWf3sQQemxJBWobj8vMqpQoULQiFnc0O/b+HoiE0+fsJPrmpPH/vPsErP23UA4ZKFTJaEBQULQN3/AApcdy8fQgvdgrjp3WH+eQPvUZBqcJEC4JyKt8I+n4Jh1bxRPJX9G9ekc//3MWMNQetTqaUyiUFekxldYWuuQViNiMrPuS9Hg2JPtOEoXM2U654IB1qX1nHgkqp/EdbCOp8N7wKtXti+/3/GHt9IrVDg3l8SgRbjpy2OplSysu0IKjz+fhAv3FQuiZFfn6Q7/uVpXignYET1nA4TsdRUKog04Kg/iugGNw5DUwmIfMHMfGeazh6IpOWL6zGJyAdEc7dypWzOqxSylO0IKjsla4Bt30Hx7ZSe+VLHJvdDHupRMreEgE+/16jcPSohRmVUh6lBUFdXM0u0PVt2DaPF8MmcOLXRgRUPUHpHpusTqaU8gItCOrS2jwJjQYw/IZ36JyxgdMraxLUMAr/yiesTqaU8jAtCOrSRODmz1h9uBlTbnmYCoejibb9H8U6/wXolcxKFSS5MWLadyJyTEQ2Z3mslIgsFpFdrn9LejuHygF7ILfMmEpCWlHm3n43Re2bSa40jiJ1o61OppTyoNxoIUwEelzw2CvAn8aYWsCfrvsqD8ssUoF+v3xKZf94phFIos+fBHcMJ7S8doKnVEHh9YJgjFkOnLzg4T7AJNffk4C+3s6hciYmBpp+Mp8XbBl0x5fHfHxILPMd7808YHU0pZSHWHUMIdQYc3Z/QwwQerEJReRhEVkrImtjY3WYR6tEx0czIXICYxzJ/EEG7xtfytj+5OM/V+v4CUoVEJYfVDbOPpYvenTSGDPOGNPCGNMiJET707HK8OXDcRgHCAwmGQG+wpf96ZMYu2yP1fGUUh5gVUE4KiLlAVz/HrMoh3JTeFQ4aZlpAOwXwyuk0AMb9wdsZvyKfUSf1m4tlMrvrOrtdB5wP/C+69+5FuVQblr/yPrzH3A4YOKNfH50K+3MKT5ZvJMPbmtsTTillEfkxmmn04BwoI6IRInIgzgLQVcR2QV0cd1X+YmPD/T+Ap/MVL4LmcasiEPsiIm3OpVSKgdy4yyjO40x5Y0xdmNMJWPMt8aYE8aYzsaYWsaYLsaYC89CUvlBmZpww1DqxC2nn/8aRv623epESqkcsPygssrnWj8BFZox3D6RyO27WbnnuNWJlCowypXjvN6Fvd3LsBYElTM2X+gzhoDMREYWmcL7v27H4dAuLZTyhIv1JuytXoa1IKicC62PdHiZro6/CD3yJ/M3aZcWSnmMOAhuuRfxy/D6qrQgKM+4/jlMaAPe95/IV7+tJTUj0+pEShUIQY0PUarTNgKqeH93rBYE5Rk2O9JnDKU4zcD48Uz956DViZTK98Q/nRLtdpJ42EHy9QMgKMar69OCoDynQhNo+yz9fZex9s+ZnE7WLi2UyonibXbjE5hKPfkGqvwF7Yd7dX1aEJRHSYeXSSlRk1cdX/PdnxusjqNUvnXgRCLFWuyj9ZEtLK++jP7iA00nQFAMoRft/S1ntCAoz7IHEHDrV5SXk4Sufp8jcdqlhVJX472F2yke6ODT+qPZhYM5ZOAXkMnj04cT46U9R1oQlOdVvpbEpoO5y2cxc3+eYXUapfKd8D0n+G1LDB9UW0H51HheIIV0gbTMNCZETiAmwTsVQQuC8orgnm9x0r8iN+57hx2HvHsgTKmCJNNhGLFgK3WKZXB91HcskUx+4d9TTjNNJsOXeedYghYE5R1+RfC7ZQxV5Rj7fhxqdRql8o3Z66LYcuQMYyr/SZHMNJ41ySD/Pp+WmcbKqJVeWbdVvZ2qQiCo7g1sqXg73aJmsTH8Thq16Wp1JKXytMTUDEb9voOe5ROpse8HpOm9bOjzRa6tX1sIyqtq3Pkhx6QMJf54DkeaHmBW6lK+XraH2PhU3g2eifj6Q6fXcnX9WhCUVwUElWBPmxFUyTzE7lmvWx1HqTzrcFwy45bv5flaRyl5cBFc/xwEe+n80ovQgqC8rk3XASz260L1neNJO7TO6jhK5Ukf/LYdHxw8mvItFK8MbZ7I9QxaEJTX+fgIQb1HctIUI37Gw5CRZnUkpfKU9QdPMTfyCB/X2YJf7Gbo8ibYA3M9xxUVBBHxEZFinlq5iDwnIltEZLOITBORAE8tW+UtbRrUZGrIs5RO2EXK0o+sjqNUnmGMYfj8rVQJctA9ZjxUagkNbrUky2ULgoj8ICLFRKQosBnYKiIv5XTFIlIReBpoYYxpANiAO3K6XJV3des3iHmZbbD//SEc3Wp1HKXyhF82RrPuYBxfh63AJ/EodH/POQqOBdxpIdQ3xpwB+gK/AtWAez20fl8gUER8gSLAEQ8tV+VB11Qozpp6r3DaEUjaT49Bpvf7d1cqL0tJz2Tkr9vpEJpCvf2TnC2Dyi0ty+NOQbCLiB1nQZhnjEkHcjwkljHmMPAhcBCIBk4bYxbldLkqb3v0xla87RiI39FI+OdLq+MoZalv/9rH4bhkPiw113ntWZc3Lc3jTkEYC+wHigLLRaQqcCanKxaRkkAfnC2OCkBREbknm+keFpG1IrI2NjY2p6tVFqtYIpDQ1nfye2YLHP8bAcd3Wx1JKUsci0/hyyW7ebj6KUL2zXWeVVSiiqWZLlsQjDGfG2MqGmNuNE4HgBs8sO4uwD5jTKyr1fETcF026x9njGlhjGkREhLigdUqqz1+Qy0+sD1MssMO854Eh8PqSErluo9+30laZibPOyZA0bLO6w4s5s5B5RIi8rSIfCwin4vI58DHHlj3QaC1iBQREQE6A9s8sFyVxxUvYufOzi15I+1uOBgOa8ZbHUmpXLXlyGl+jDjEyDp7CIhZC52GgX+w1bHc2mW0EAgDNgERWW45YoxZBcwC1rmW7QOMy+lyVf5wb5uq/BPcnQh7M8wyR2HzAAAgAElEQVQfb8Kp/VZHUipXGGMYMX8bZQMMfY+Pg9CG0PQ/e8st4U7ndgHGmOe9sXJjzBvAG95Ytsrb/H1tvNi9Lk/NeIBlRV/BPu9puG+uZafbKZVbFm89SvjeE/zUcBU+uw5B3zHgY7M6FuBeC2GyiAwWkfIiUurszevJVIHXu3EFSlaozqdyL+xbBuu+tzqSUl6VluHg3YXbaFEmnaYHJkCdG6F6B6tjneNOQUgDRgHh/Lu7aK03Q6nCwcdHGHpjPb5MaMeREi1g0TA4fdjqWEp5zffh+9l/IonPQhciGcnQ1TsD3VwtdwrCC0BNY0yYMaaa61bd28FU4dC2Zhna1w5lcNz9mMx0mP8cmBxf5qJUnnMyMY3P/tzFXWEJVNw7E1oOhjI1rY51HncKwm4gydtBVOH1Ss+6bE0tzZ8VHoFdv8OmmVZHUsrjPv1jJ0lpGbzqOxn8i0GHl62O9B/uHFROBCJFZAmQevZBY8zTXkulCpV65YvRr2klntwIGyq3wP/Xl6F6Rwgqa3U0pTxi19F4pq46yBt1oii6bwX0eB+K5L1Dse60EH4G3gFW4sHTTpXK6oVutXHgwydFnoa0JFj4otWRlPKYdxZuo5if4e7T46B0TWj5kNWRsnXZFoIxZlJuBFGFW4USgQxqW42xy/cw8PpnCF3zAWz5Ga7pa3U0pXJk2c5Ylu6I5YeGkdh27YY7p4PNbnWsbLlzpfI+Edl74S03wqnC5bGONSgeaGdIdEco3xgWvkjMsa10mNiBmIQYq+MpdcUyMh2MmL+Va0o5aBP1DVTrALV7WB3rotzZZdQCaOm6tQM+B6Z4M5QqnIoH2nmqUy2W7o4joskISD7FgRl38tfBvxi+LG+dnqeUO6atOcSuYwmMqfgHkhwH3d/J0xdfutO53Ykst8PGmE+Bm3IhmyqE7mldhUolA3ntH+FMy4dpdWI/PRw+TIicoK0Ela+cTk7nk8U76VM5map7pkKze6FcQ6tjXZI7u4yaZbm1EJFHce/sJKWumL+vjZe612Fr9BnuOnqI7Tj4EH+MI1NbCSpfGbNkN6eS0hheZAbi6w83DLM60mW5s8vooyy394DmQH9vhlKF282NKlCrfDoLD8xkGCnUw8atmUZbCSrfOHAikQl/72NInWMUO7AI2j0PwaFWx7osd84y8sTYB0q5zcdHWLluLqaag5/IYAOZvIEf01PSqT5wOEkzx1gdUalLem/hdvxt8GDieCheGVo/bnUkt7izy+gZESkmTuNFZJ2IdMuNcKrwSgqMBMnACLxOKrWwca/NkFx6pdXRlLqkf/ae4LctMXxaZyv22M3OYTHtgVbHcos7u4wGGWPOAN2A0sC9wPteTaXU2PXYvzhNlaT5LF8eydojTXj9VB3s36yyOplSF+VwGEYs2ErNYobOR8ZBpWuhwa1Wx3KbOwXh7DlSNwLfG2O2ZHlMKa9JP16MxM2VKNbsIG+tepFqJQ/yQJOpVsdS6qJmr4ti8+EzjAlbgSQehe7v5unTTC/kTkGIEJFFOAvC7yISDOgguCpXxK2oDUB4pcqEH2rJsPYfQkbqZeZSKvclpmYw6vcddKmQRu29E6HBbVC5pdWxrog7BeFB4BWgpTEmCfADBnpi5a7xmmeJyHYR2SYibTyxXFVwZMYHciYijKINDvP2umepUjwKIrQ3FZX3jF22h2PxqYwsMce5C6XLm9YGugruXJjmMMasM8bEue6fMMZs9ND6PwN+M8bUBRoD2zy0XJXPhWY5Q+/MPzVwpPoSUTOE8CPXwYqPID3ZunBKXeBwXDJjl+/lydpxlN47F9o8CSUqWx3rirnTQvAKESkOtAe+BTDGpJ0tOkrFxDjHyTEGMpP9GHZLTYrUOE6x+5+EhBhY+53VEZU654PftgOGp9InQFAoXP+s1ZGuimUFAagGxAITRGS965TWohdOJCIPi8haEVkbGxub+ylVnnD/dWGULx7A0MgSmGrt4a9PIC3R6lhKsf7gKeZGHmFUvT34R6+BTsPAP9jqWFfFnesQPhKRa7ywbl+gGfCVMaYpzoF4XrlwImPMOGNMC2NMi5CQEC/EUPlBgN3Gc11rs+FQHP9UeRQSY2H1N1bHUoWcMYbh87dSMUjodWyss6+iJndbHeuqudNC2AaME5FVIvKoa1ePJ0QBUcaYsyeWz8JZIJTK1q3NKlE7NIihEUVx1OgMf38GqfFWx1KF2C8bo1l3MI6vaqzC5/Qh6PYO+NisjnXV3DmoPN4Y0xa4DwgDNorIDyKSoy4tjDExwCERqeN6qDOwNSfLVAWbzUcY0qMu+44n8nvIIEg+Cau+tjqWKqRS0jMZ+et2rgvNpOG+b6HOjVC9g9WxcsStYwgiYgPqum7HgQ3A8yIyPYfrfwqYKiIbgSbAuzlcnirgOtUty7VhpXhtbQAZNbvDytGQrOciqNxRrpzzOjMRCG2/j8NxyXRevYCM5GTomv9743XnGMInwA6cF6a9a4xpbowZaYy5GWiak5UbYyJdxwcaGWP6GmNO5WR5quATEYb0rMvxhFRmBt8LKafhn6+sjqUKiaNHnf/6FE2heOvdhB1M4IFaP/LFmoehTE1rw3mAOy2EjUBjY8wjxpjVFzx3rRcyKXVJzauWpMc15RgRYSe11k3wz5eQdNLqWKoQKdFuJ+KbybCAycSlFOftZS9bHckj3CkIG4A6FwyUU0NEfI0xp70dUKnsvNSjDikZDr71vcN5YDn8C6sjqULCXvY0QY0O0WbfYbpUWcFby14hLqWk1bE8wp2C8CXwDzAO+AYIB2YCO7QbbGWVGiFB9G9RmU82+pJYqzf88zUkHrc6lirwDKU6bcWknOLNOsPYfrIaX6190OpQHuNOQTgCNHXt62+O87jBXqAr8IE3wyl1Kc92qYXNR/g0vR9kJMPfn1odSRVwgbWOElD1JP0cX1HXnsqLx6uS4bBbHctj3CkItV1dXgNgjNkK1DXG7PVeLKUuL7RYAA9dX51vttuJq9EHVo+H+KNWx1IFVGpGJmW6bKNIXCyvl9rEH2SwoPpiCIo5r++t/MydgrBVRL4SkQ6u25eux/yBdC/nU+qSHu5QnZJF7IxI6A2Zac4uLZTygu9XHsCnWBKf1f6YYIGnScEvIJPHpw8npoAM9e1OQbgf2A0867rtBR7AWQx0vGVlqWIBdp7sVItZ+/2JqXaLs9O7M0esjqUKmBMJqXz+5y7uq7yTrmcO8BFpbBMHaZlpTIicQExCwagIlywIrgvSxhtjPjLG3OK6fWiMSXJ1i52QSzmVuqh7WlehUslAhp7ogTGZzu6xlfKgT/7YSWp6Gg/Gf8JBDMP5d5CmTJPJ8GX5/6I0uExBMMZkAlVFxC+X8ih1xfx9bbzYrQ7/O1qEA1VucQ6gE3fI6liqgNgRE88Pqw7yefU1VE05zTMkk5RlVMy0zDRWRq20LqAH+boxzV7gbxGZh7NHUgCMMR97LZVSV6h34wqMXb6XF2K6MUvmIstHQe/PrY6l8jljDCMWbKWG/xm6Hx0Ptbox564f89U4yVfCnWMIe4D5rmmDs9yUyjN8fIRXetYlIq4o2yr0g8ipcHKf1bFUPrd0Rywrdh1nbOgcxJEBPUcW2GIAbrQQjDFvAYhIEdeYykrlSe1rlaFtzdI8e7gTv/v87Gwl9P3S6lgqn0rPdDB8wVZuK7GL6kd/h45DoVR1q2N5lTud27URka3Adtf9xq5TT5XKU0Sc3WPvTApiXcgtsGEaHN9tdSyVT0395wBRsXG8ZZ/oLARtn7E6kte5s8voU6A7cALAGLMB51jISuU5jSqVoFej8jwT1RFj84dlI62OpPKhuKQ0PvljFyPKLqFo/D64cRTYA6yO5XVujYdgjLnwlI1ML2RRyiNe6l6HmMxirCh5C2yaCce2Wx1J5TOf/bmL4imHuS1xGtTvAzW7WB0pV7hTEA6JyHWAERG7iLyIc1hNpfKkqqWLcnerKjx/uAMOexFY+p7VkVQ+sic2gcnhBxgbMhMfH1/oXng+P+4UhEeBJ4CKwGGcI5s94akAImITkfUiMt9Ty1Tqqc61SPYtwe9BfWHrzxCz2epIKp94d8E2etrXU+/M39DxFShe0epIucadMZWPG2PuNsaEGmPKGmPuMcac8GCGZ9AWh/KwMkH+DG5fnSHRHci0B2srQbllxa5Y/t5+iHcDJ0NIPWj9mNWRcpU7ZxmFiMhQERknIt+dvXli5SJSCbgJGO+J5SmV1eB21fELKsVs/z6wfT4cWW91JJWHZWQ6GDF/G0ODFhCcEg29PgZbwena2h3u7DKaCxQH/gAWZLl5wqfAy4DjYhOIyMMislZE1sbGxnpotaowKOrvyzOdazH8eEfS/YrDEm0lqIubvuYQ6cd2cE/mXGh8J1S9zupIuc6dglDEGDPEGPOjMWb22VtOVywivYBjxpiIS01njBnnGpynRUhISE5XqwqZO66tQunSZZgsfWDX7xC11upIKg86k5LOx4t28FnwFMS/CHR92+pIlnCnIMwXkRu9sO62QG8R2Q9MBzqJyBQvrEcVYnabDy91r8uHpzuS6lcSlrxjdSSVB33xv920TV1Gw7RIpPPrEFTW6kiWcKcgPIOzKKSIyBkRiReRMzldsTHm/4wxlYwxYcAdwP+MMffkdLlKXejGhuWoVSmUcZk3w57/wYFwqyOpPGT/8URm/r2FdwKnQYWm0Hyg1ZEs485ZRsHGGB9jTIAxppjrfrHcCKeUJ4gIQ3rWZUziDST5ldZWgjrPe79u41nf2QRnnISbPgIfm9WRLOPOWUYiIveIyGuu+5VF5FpPhjDGLDXG9PLkMpXK6roaZWhVuxKj026G/Stg33KrI6k8IHzPCQ5uXc298hvSYhBUbG51JEu5s8voS6ANcJfrfgIwxmuJlPKSIT3q8l1qR+LtIbDkXTDG6kjKQpkOw4hfNjMyYBJSpBR0fs3qSJZzpyC0MsY8AaQAGGNOATqCmsp36lcoxk1NqvFxys1wMNx5PEEVWrMjoqgfO59GZjvSbTgElrQ6kuXcKQjprrGVDTgvVOMS1w0olZc917U2Pzpu4JQ91HksQVsJhVJCagZjf1vLa37TMVXaOK87UG4VhM+BOUBZEXkH+At416uplPKSyqWKcEebmnyQdDMcjoBdi6yOpCzw1dLdPJj6PcEkIjd9VKBHQbsS7pxlNBXn1cTvAdFAX2PMTG8HU8pbnryhJr/5duKYb3ltJRRCh04msXrFIu7wXYK0fgxCr7E6Up7h7ngI240xY4wxXxhjtCM6la+VLOrHQx3rMDKpD0RvgO2e6olF5Qcf/LqFN23fYoLKOXszVee4VRCUKmgGta1GeNFOHLZVxCx5Bxx6WKwwWLv/JCW3TuYa2Y+t5/vgH2x1pDxFC4IqlAL9bDzdtR4jk/six7Y6x0xQBZrDYRg97y9ets8ks9oNzpHQ1Hm0IKhC67bmldhWqjP7fSpjlr4PDh0ZtiD7OfIwfWO/JtAnHVsvPZCcHS0IqtDytfnwYs9r+CDlFuT4Dtic4058VR6VlJbBHwtnc4vtb3yufw5K17A6Up6kBUEVat3qh3KsUnd2URXH0veJPn2IDhM7EJMQY3U05UHfLNnBc2ljSQ2qjLR73uo4eZYWBFWoiQhDbqzPqLR++Jzcw+KfH+Kvg38xfNlwq6MpD4k+nUz636Op5XMY/94fgz3Q6kh5lhYEVei1DCvFr/tvYkNmFa7fG46Pw8GX4ROQ4BjKlbM6ncqpcb8s53H5ieQaPaF2N6vj5GlaEJQCji6qy1sEUV2EYfiDZEL74Rw9anUylRORh+JotWMUvjYh8OZRVsfJ87QgKAWkpyYwx2c9k0hjGH50sGVC0wkQpMcS8itjDAtmT6SHbQ2m/ctQorLVkfI8LQhKAXQYDg7DE6SwBwdTCaS0q5Wg8qeF6/dxz8kxnA6qjv/1T1kdJ1+wrCC4BtpZIiJbRWSLiDxjVRalqBQOvmkkCgwgmTIIE2w2qPy31cnUVUhJz+Togveo6nOMoH6fga/22O8OXwvXnQG8YIxZJyLBQISILDbGbLUwkyqsxq4/9+e+Nrt494bRvGWfxNORj1gYSl2tWYuWcXfGHGKr9yGkenur4+QblrUQjDHRxph1rr/jgW1ARavyqMItNPTfv0+H1+SrHfewKKM5o7q9BkfWX3xGleccO51M2Oo3cdj8COmnB5KvRJ44hiAiYUBTYJW1SVRhFRPj7AXbeRN2TW7K6GLPcMqnGBk/DoTUeKsjKjf9Pmsc18sGkq9/BYJDLz+DOsfygiAiQcBs4FljzJlsnn9YRNaKyNrY2NjcD6gKpeKBdkbecwPPZz6JT9wBHL88p+Mm5ANb9x2my8FPiSlSm1IdHrc6Tr5jaUEQETvOYjDVGPNTdtMYY8YZY1oYY1qEhITkbkBVqNWvUIzb+vXnk/R++GyeCRumWR1JXYIxht2zXiNUThF822iwWXmINH+y8iwjAb4FthljPrYqh1KXckvTSpxp+TThmfXJ+OV5OL7L6kgqi3LlnJ2WSnA0jZ5uxo0Jc5i0vx81rmttdbR8ycoWQlvgXqCTiES6bjdamEepbL3aqyHflP0/zmT4kjrtPkhPsTqScjl3JXnHNxlTeidx2Hhx5gd6hflVsvIso7+MMWKMaWSMaeK6LbQqj1IX4+frwzv3deUt25P4n9hK2m+vWh1JZRUUzcCmk2mPLy+bZE76ZFidKN+y/KCyUvlB+eKB3HH3YMZn3ohfxHjMtl+sjqRcmt/xCF/4+LKEDCaaDL26PAe0ICjlpjY1SkPnN9joqEbq7Mch7pDVkQq9Ctcu5ceKSziJ4Q6SMb5p2gdVDmhBUOoKPNihDrPC3iY9PZ0zU++HTN09YZU/txxhYvf7qWiEW0nmmLhOC9Y+qK6aFgSlroCI8PLdN/JZ4OMUi40gYdEIqyMVSv/sPcHOGf9HV584npQUVkuW8bB90/CtttK6cPmYnqir1BUK8vfljkHPMXvMOm5Z9SnpNTtir9XR6liFxubDp5k26Us+8/mZlEb38E2/MXxjdagCQlsISl2FmmWDCer7EXsd5UmZMQgS9Cr63LD7WAKvfzuH9+QL0so1JaC3XsLkSVoQlLpK3ZvWYEmjkfilnyHm+4HgcFgdqUA7HJfMI+OX8LFjJP6BQfjdORV8/a2OVaBoQVAqBwbe0ospJR6h3LEVxCz6yOo4BdbxhFTu+yacoWmfUVWOYhswCYpr58iepgVBqRzwtfnQ+8HXWCKtKPPPeyTs0Q57Pe1MSjr3fbuaXvHT6cwapNsICLve6lgFkhYEpXIopFgAJe8cx1FTkqRp9+NIirM6UoGRnJbJgxPXUC52Bc/6/AgNb4fWj1kdq8DSgqCUBzSpHcbGVh9RKv0ou797SLvK9oC0DAePTY3g6IHtfB34NRLaAG7+3NmbnfIKLQhKeUiPnn34reyD1D6+mB2/fWl1nHwt02F4YeYGVu04xNwyX+FnExgwGfyKWB2tQNOCoJSHiAidH3qPdb5NqLLqTaJ36dCbV8MYw+tzN/PLhsPMq/IjJeN3wa3fQqlqVkcr8LQgKOVBgf52Qu6dSBKBpE6/n5SkBKsj5Tujft/B1FUHGV97DbWO/QadhkGtLlbHKhS0ICjlYZWrVuNA+48JyzzA+vE6jOOVGLtsD18u3cPQ+sfpfGg01O0F7V6wOlahoQVBKS9o1uk2Vle4lzYn5/LX3PFWx8kXpq8+yHu/bueeejYGx7yNlK4Bfb/Sg8i5SAuCUl7SfODH7ParS6N1r7F16yar4+RpCzZG839zNtGlVnHeTh2JZKTCgKkQUMzqaIWKpQVBRHqIyA4R2S0ir1iZRSlPs9n9CLl/Cj4CjpmDOHkm0epIedKynbE8O2M9zauU5OvS0/E5sg5u+RpCalsdrdCxrCCIiA0YA/QE6gN3ikh9q/Io5Q3FK9biZKdRNDA7+fub58h06PUJWUUcOMmjkyOoWTaY75tsxTdyMrR7Eer1sjpaoWRlC+FaYLcxZq8xJg2YDvSxMI9SXlGl/T3sqXwbN535kZ9mTrY6Tp6xLfoMAyesoVzxAH7o4UORxa9Ajc5ww1CroxVaVhaEikDWMQijXI+dR0QeFpG1IrI2Nla7GFb5U417RxMbUJWOW4exbN0Wq+NYbv/xRO79djVF/HyZekcYJec/6Oys7tbx4GOzOl6hlecPKhtjxhljWhhjWoSEhFgdR6mr41eEEvdNoZgk4zv3MfbFxludyDIxp1O4e/wqMh0OpgxsSoVFj0FyHAyYAkVKWR2vULOyIBwGKme5X8n1mFIFkn/FhiR1GkFb2cDUd4bh45eBCOdu5cpZndD7Tiamcc+3qzidnM6kQddSM3IkHFwJvUdDuYZWxyv0rCwIa4BaIlJNRPyAO4B5FuZRyutKtnuY2ft7MqT4ZLr2/xoe6ABBMQAcPWpxOC9LSM1g4ITVHDyZxDf3taDRid9h1dfQ+nFodLvV8RQWFgRjTAbwJPA7sA340RijO1dVwSbCg9O/5khyKGNrvE3xqiug/XCrU3ldSnomgyetZfORM3x5VzPaFImCX56GqtdD17etjqdcLD2GYIxZaIypbYypYYx5x8osSuWW06klGPDzR1QkhckEENz8WyhecPeWZmQ6eGraesL3nuDD2xvRJcwOM+6BIqXh9olgs1sdUbnk+YPKShVEq2rP5zmTwU34ssXHzi2PDsAv9LTVsTzO4TC8PHsji7ce5a3e13BL4/Iw+0GIj4H+kyFITxTJS7QgKJXbgqKhyQTG2JK5jiROY/gpYBMzHurHd4vW5PuL18qVO3ug3FCm21Z+WneYuBW1GdIvDP43HPb8D278ECo1tzqquoAWBKVyWWCP4SAOAFZJJs1I5A1HOjfaIuj7d1++/Owdok7m324uzh4cL952F8Va7OfMmmqcXlmTtqXmwl+fQPMHoPn9lmZU2dOCoFQuq9MlHHzTzt1PF3jblsydZSpiStXgqdOj2P/5jSxaudrClFfPXiaesretpsT1u0jYVIlT/6tHvTI7mNjncajUEnp+YHVEdRG+VgdQqrBZ/8glRlJzZHJq6Riar3gHx++9mBX5MF3vH0bxogG5F/AqHTuTwseLd1J+4CEcab6cWlKXM2uqUcz/DHMG3E1SeiDB/b8HX3+ro6qLEJOPBgNv0aKFWbt2rdUxlPK6jBP7OTzlMaqeWslmqU1Gr9E0ad7a6ljZSkrLYNzyvYxbvpf0TAcn/gnj9MqaOFL8EBzMGXA3N9ZaROfv57H8QFur4xZKIhJhjGlxuem0haBUHuRbOoyqTy/kwNIJVF72OoHzbmTFuoG0uu8d/PzzRmsh02GYFXGIjxbt5Fh8Kjc2LMfL3etSLaSoc4KgaF59sCN9SsTw9K8jWXFQi0Fepy0EpfK4xJPR7Pr+SZrE/cF+nyrY+o6mcqOOlmZatjOWdxdsY8fReJpWKcGwm+rRvKqzH6Jy5ZwHlnve1Yf5NZcw9UR17huzntBQISbG0tiFlrstBC0ISuUT6/+YTvm/hlLWnGR71buod/dIxD84VzNsiz7Duwu3sWLXcaqUKsIrPevSs0E55Owwl8bAsa3ER04lM/wL9uGgi6+DLc/upVxQIeisKY/SgqBUARR7PJYNk56nS/w8jttC8e37GSUa9vT6emNOp/Dx4h3MjIiiWICdpzvX4p7WVfD3tTmLwJH1sG0ebJ0HJ/fgAJZJJgNNEtG+dh5q+hBjbhrj9Zwqe1oQlCqgjDH89uvP1F41lBpyhCNV+1BhwKde6To6ITWDccv2MG7FXhwOuP+6qjx5Qy2KB9ggarWzAGz7BU4fBLFBtfacrt6BRkuHcjAz5dxyAn0D2fuMthKsogVBqQJu9+FY1kx+lduSZ5HqG4y91yj8m9zuvEw4hzIyHfy4NoqPF+/keEIqvRqV5+WuNakS72oJbJsPCTFg84ManaBeb6jTE4qU4vEFj/Pt+m9Jy/z3Wgs/m5+2EiykZxkpVcDVrBhClRe/ZtLcXrTc8AaN5w7m9LrpFL9ttHP0satgjGHpjljeXbiNXccSaF0liOk3nKHm8e9gwkJIOgH2IlCzC9TvA7W6QUCx85YRHhV+XjEASMtMY2XUyqt+rSp3aAtBqQIgfNcx1kx/h8EZP2DztWPr9ha2lg+Cj/udEWw+fJr3ft3G2t3R3F58O4+FbqXC0aVI6hnwC4Y6PZwtgZpdwK+IF1+N8jTdZaRUIXM6KZ1PZi6i8+53aWfbTEqFVgT0GwNlal1yviNxyYz+dT3xmxfS276WG2yR2DOTIbAk1LkJ6veG6h31CuN8TAuCUoXUz+uiWDt3DC8xiSBbOj4dhyBtnyE66Th3zL6DGbfNoFxQOeLjYlkxfzL+O+dzvWzEX9JxFC2LT71ezpZA2PU6VkEBkacLgoiMAm4G0oA9wEBjTNzl5tOCoJR7ok4l8dYPS+jz/+3df6zVdR3H8efLKyICgzGuP5KLv8IWMoSAjFUCwxElCyz6oVS7k0lkttxK0m6pG9FyNKdpzVDYXdvNSDAzshAHRWuDMIK6hDhsMGygYEoaLuTed398P3DvpXu5v86533POfT02xvl+z/f7Pa8P93Le5/v5nu/nc+hB5lRtZeerV7HwSA3737uGeftn8ulBVUw/fysD1MTrZ1dz9ri5DJ34Sai5Bs6qyju+FVipF4RZwMaIOCHpPoCI+EZn+7kgmHVdU3Pw480vsf23P2XpOSs5X6+DoAqxr3kk696Ywazaz3HlxGkF+WaSla6SLghtAkg3APMjYkFn27ogmHXfwAuPMuLzN3Hb4E000cxamtn14o00PV5PhAtBf1BOXzu9GVjd0ZOSFgGLAEaPHt1XmcwqxvH/HOPQwI18Sy03inH5EzDkPsA3ilmLok2QI+k5SY3t/Jnbaps64ATQ0NFxImJFREyOiMnV1Z5/1azbprXM0HaKmr9OnT8AAAX6SURBVODapfnksZJVtDOEiLjuTM9LqgXmADMj734rs0o2qu0MbUC2XOMbxaytXLqMJM0GlgDTIuJYHhnM+osLnvrLqXmO26y/AHikz+NYCcvrGsLDwEBgQxo2d0tELM4pi1lF8xwE1lW5FISIeHcer2tmZh0r2kVlMzMrLy4IZmYGuCCYmVnigmBmZkAJDF3RHZIOA/uLdPiRwJEiHTsPldYecJvKhdtUei6JiE7v7C2rglBMkp7vylgf5aLS2gNuU7lwm8qXu4zMzAxwQTAzs8QFocWKvAMUWKW1B9ymcuE2lSlfQzAzM8BnCGZmlrggmJkZ4IJwiqSlkv4qaYekZyW9K+9MvSVpuaQXUrt+IWl43pl6S9KnJO2S1CyprL8GKGm2pD2S9kq6M+88vSVplaRXJTXmnaUQJNVI2iTp7+l37qt5Zyo2F4QWyyNifERMANYBd+cdqAA2AOMiYjzwInBXznkKoRH4BLA57yC9IakK+CHwUWAscKOksfmm6rV6YHbeIQroBPC1iBgLfAD4cgX8jM7IBSGJiH+3WhwMlP3V9oh4NiJOpMUtwKg88xRCROyOiD155yiA9wN7I+IfEXEc+Bkwt5N9SlpEbAb+lXeOQomIgxGxPT1+E9gNXJxvquLKa4KckiRpGfAF4CgwI+c4hXYzsDrvEHbKxcCBVssvA9fklMU6IelSYCKwNd8kxdWvCoKk54AL23mqLiJ+GRF1QJ2ku4DbgHv6NGAPdNamtE0d2elvQ19m66mutMmsr0gaAqwFbj+tJ6Hi9KuCEBHXdXHTBuAZyqAgdNYmSbXAHGBmlMlNJ934OZWzfwI1rZZHpXVWQiQNICsGDRHxZN55is3XEBJJY1otzgVeyCtLoUiaDSwBPh4Rx/LOY21sA8ZIukzSOcBngadzzmStKJvwfSWwOyLuzztPX/CdyomktcB7gGayIbYXR0RZf2KTtBcYCLyWVm2JiMU5Ruo1STcADwHVwBvAjoj4SL6pekbSx4AHgCpgVUQsyzlSr0h6HJhONlT0K8A9EbEy11C9IOlDwB+Av5G9LwB8MyKeyS9VcbkgmJkZ4C4jMzNLXBDMzAxwQTAzs8QFwczMABcEMzNLXBCsYkgaLunWVsvTJa3r5jFqiz3SraR7JX29mK9h1hMuCFZJhgO3drrVmdUCZT/0uVlPuCBYJfkecEWa02J5WjdE0po0L0RDuvsUSZMk/V7SnyWtl3SRpPnAZKAhHWOQpLslbZPUKGnFyf1PkjRM0n5JZ6XlwZIOSBog6Za0705JayWdd3pgSb87Oa+DpJGS9qXHVWk+i21pPosvpvUXSdqc8jVK+nCR/i2tH3JBsEpyJ/BSREyIiDvSuonA7WRzDlwOfDCNT/MQMD8iJgGrgGURsQZ4HliQjvE28HBETImIccAgsnGhTomIo8AOYFpaNQdYHxHvAE+mfa8mGzp5YTfashA4GhFTgCnALZIuA25Kx58AXJ1e26wg+tXgdtYv/SkiXgaQtAO4lGzIi3HAhvSBvwo42MH+MyQtAc4DRgC7gF+dts1q4DPAJrIxiX6U1o+T9B2yrqwhwPpu5J4FjE9nLQDDgDFkYyCtSkXtqYhwQbCCcUGwSvffVo+byH7nBeyKiKln2lHSuWRv7pMj4oCke4Fz29n0aeC7kkYAk4CNaX09MC8idqZRZ6e3s+8JWs7UWx9bwFci4v+KiKRrgeuBekn3R8RPztQOs65yl5FVkjeBoV3Ybg9QLWkqZEMcS7qqnWOcfIM+ksbEn087IuItsk/uDwLrIqIpPTUUOJg+zS/oIMs+siLCacdfD3wp7YukK9P1iUuAVyLiUeAx4H1daK9Zl/gMwSpGRLwm6Y9pkvffAL/uYLvjqSvmB5KGkf0/eICsO6geeETS28BU4FGyeZwPkb3pd2Q18ARtzwK+TTbD1uH0d3vF6vvAzyUtOi3vY2TdW9vThezDwLx0/DskvQO8RTbDn1lBeLRTMzMD3GVkZmaJC4KZmQEuCGZmlrggmJkZ4IJgZmaJC4KZmQEuCGZmlvwPVRpT9UqqWTYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(thetas, values2, 'bs', label = 'simultaneous')\n",
    "plt.plot(thetas, values2)\n",
    "plt.plot(thetas, values, 'g^', label = 'naive')\n",
    "plt.plot(thetas, values)\n",
    "plt.xlabel('theta values')\n",
    "plt.ylabel('energy sums')\n",
    "plt.title('simultaneous vs naive for simulator')\n",
    "plt.legend(loc='best')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
